43. Dijkstra's Algorithm: Detailed Implementation Steps

Let's formalize the steps for Dijkstra's:

1. Initialization: Create a distance array dist (all set to infinity, source set to 0) and a set visited (empty).
2. Priority Queue Setup: Insert the source node (distance 0) into a Min Heap.
3. Iteration: While the Min Heap is not empty: a. Extract the node U with the minimum distance (the greedy step). b. If U has already been processed (in the visited set), continue. c. Mark U as visited. d. Relaxation: For every neighbor V of U: * Calculate the tentative new distance: new_dist = dist[U] + weight(U, V). * If new_dist < dist[V], update dist[V] to new_dist and insert/update V in the priority queue.

• Complexity: With a Fibonacci heap, O(E + V log V). With a standard Binary Heap (more common), O((V + E) log V).